Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 1-11.

Title: Simulation of incompressible flows with heat and mass transfer using
  parallel finite element method

Authors: Jalal Abedi (Clark Atlanta Univ., Atlanta, GA, USA)
Jalal Abedi (Clark Atlanta Univ., Atlanta, GA, USA)

Abstract: 
The stabilized finite element formulations based on the SUPG
(Stream\-line-Upwind/Petrov-Galerkin) and PSPG (Pressure-Stabilization/Petrov-Galerkin) methods
are developed and applied to solve buoyancy-driven incompressible flows with heat and
mass transfer. The SUPG stabilization term allows us to solve flow problems at high
speeds (advection dominant flows) and the PSPG term eliminates instabilities associated
with the use of equal order interpolation functions for both pressure and velocity. The
finite element formulations are implemented in parallel using MPI. In parallel
computations, the finite element mesh is partitioned into contiguous subdomains using
METIS, which are then assigned to individual processors. To ensure a balanced load, the
number of elements assigned to each processor is approximately equal. To solve
nonlinear systems in large-scale applications, we developed a matrix-free GMRES
iterative solver.  Here we totally eliminate a need to form any matrices, even at the
element levels. To measure the accuracy of the method, we solve 2D and 3D example of
natural convection flows at moderate to high Rayleigh numbers.

Published February 28, 2003.
Math Subject Classifications: 65C20, 81T80.
Key Words: Finite element method; parallel simulation;
contaminant dispersion; free convection.